A structural and a functional aspect of stable information processing by the brain

In this paper a model of neural circuit in the brain has been proposed which is composed of cyclic sub-circuits. A big loop has been defined to be consisting of a feed forward path from the sensory neurons to the highest processing area of the brain and feed back paths from that region back up to close to the same sensory neurons. It has been mathematically shown how some smaller cycles can amplify signal. A big loop processes information by contrast and amplify principle. It has been assumed that the spike train coming out of a firing neuron encodes all the information produced by it as output. This information over a period of time can be extracted by a Fourier transform. The Fourier coefficients arranged in a vector form will uniquely represent the neural spike train over a period of time. The information emanating out of all the neurons in a given neural circuit over a period of time will be represented by a collection of points in a multidimensional vector space. This cluster of points represents the functional or behavioral form of the neural circuit. It has been proposed that a particular cluster of vectors as the representation of a new behavior is chosen by the brain interactively with respect to the memory stored in that circuit and the synaptic plasticity of the circuit. It has been proposed that in this situation a Coulomb force like expression governs the dynamics of functioning of the circuit and stability of the system is reached at the minimum of all the minima of a potential function derived from the force like expression. The calculations have been done with respect to a pseudometric defined in a multidimensional vector space.Comment: Sixteen pages, two figures. Accepted for publication in Cognitive Neurodynamics (Springer

Behavioral response to strong aversive stimuli: A neurodynamical model

In this paper a theoretical model of functioning of a neural circuit during a behavioral response has been proposed. A neural circuit can be thought of as a directed multigraph whose each vertex is a neuron and each edge is a synapse. It has been assumed in this paper that the behavior of such circuits is manifested through the collective behavior of neurons belonging to that circuit. Behavioral information of each neuron is contained in the coefficients of the fast Fourier transform (FFT) over the output spike train. Those coefficients form a vector in a multidimensional vector space. Behavioral dynamics of a neuronal network in response to strong aversive stimuli has been studied in a vector space in which a suitable pseudometric has been defined. The neurodynamical model of network behavior has been formulated in terms of existing memory, synaptic plasticity and feelings. The model has an analogy in classical electrostatics, by which the notion of force and potential energy has been introduced. Since the model takes input from each neuron in a network and produces a behavior as the output, it would be extremely difficult or may even be impossible to implement. But with the help of the model a possible explanation for an hitherto unexplained neurological observation in human brain has been offered. The model is compatible with a recent model of sequential behavioral dynamics. The model is based on electrophysiology, but its relevance to hemodynamics has been outlined.Comment: Submitted to journa